Abstract
In this paper, we extend the model developed in part-I of this work to include the effects of the back-end-of-line (BEOL) metal layers and test its validity against on-wafer measurement results of SiGe heterojunction bipolar transistors (HBTs). First we modify the position dependent substrate temperature model of part-I by introducing a parameter to account for the upward heat flow through BEOL. Accordingly the coupling coefficient models for bipolar transistors with and without trench isolations are updated. The resulting modeling approach takes as inputs the dimensions of emitter fingers, shallow and deep trench isolation, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are first validated against 3D TCAD simulations including the effect of BEOL followed by validation against measured data obtained from state-of-art multifinger SiGe HBTs of different emitter geometries.
Highlights
Back-end-of-line (BEOL) metal layers have non-negligible impacts on the overall thermal behaviour in bipolar transistors [1,2]
We extend the model of [11] to include the effects of heat flow through the BEOL metal layers in order to be able
Symbols are obtained after substituting measurement data ([22]) while the solid and dash lines results after inserting self-heating and thermal coupling model values in the equation. In this part we extend the already developed physics based scalable model of part-I [11] for the depth-dependent substrate temperature including the effect of BEOL heat flow by introducing only one additional parameter
Summary
Back-end-of-line (BEOL) metal layers have non-negligible impacts on the overall thermal behaviour in bipolar transistors [1,2]. In part-I of this work [11], considering the heat flow only through the FEOL substrate, we have reported physics-based geometry-scalable models of the static thermal coupling coefficients for multifinger SiGe HBTs with and without trench isolation. In this part, we extend the model of [11] to include the effects of heat flow through the BEOL metal layers in order to be able.
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